System and method for generating a map for electromagnetic navigation

ABSTRACT

Systems and methods are provided for generating a high density (HD) map for identifying a location and/or an orientation of an electromagnetic (EM) sensor within an EM volume in which an EM field is generated by way of an antenna assembly. A measured EM field strength at each gridpoint of a set of gridpoints of the EM volume are received from a measurement device. An EM field strength at each gridpoint of a second set of gridpoints of the EM volume is calculated based on a geometric configuration of an antenna of the antenna assembly. The HD map is generated based on the measured EM field strength at each gridpoint of the first set of gridpoints and the calculated EM field strength at each gridpoint of the second set of gridpoints.

BACKGROUND Technical Field

The present disclosure generally relates to electromagnetic navigation,and more particularly to systems and methods for generating a map forelectromagnetic navigation and identifying a location and/or anorientation of a sensor based on the map.

Discussion of Related Art

Electromagnetic navigation (EMN) has helped expand medical imaging,diagnosis, prognosis, and treatment capabilities by enabling a locationand/or an orientation of a medical device and/or of a target of interestto be accurately determined within a patient's body. Generally, anantenna generates an electromagnetic (EM) field in an EM volume, asensor incorporated onto a medical device senses an EM signal orstrength based on the field, and the EMN system identifies a sensorlocation based on the sensed EM strength. The EM strength at eachlocation in the EM volume is previously measured or mapped to enable thesensor location to be identified in the EM volume by comparing thesensed EM strength and the previously measured EM strength.

In some cases, it may be desirable for the sensor to be a small-sizedsensor, such as a single-coil sensor, because, for instance, a smallsized sensor may be navigable to additional locations (e.g., narrowerportions of a luminal network) within the patient, to which alarger-sized sensor may not be navigable. Additionally, in contrast tolarge-size sensors which sometimes must be removed from the patientduring a procedure to make room in a working channel for other tools,the small-sized sensor may remain within the patient throughout theprocedure without interfering with the other tools, thereby facilitatingEMN functionality throughout the procedure.

To enable a small-sized sensor such as a single-coil sensor to beaccurately located within an EM volume, it may be necessary to generatemultiple (for instance, 6 or more) geometrically diverse EM fieldswithin the EM volume. However, because each of the EM fields wouldrequire generation of a measured mapping of the corresponding EMstrength at each location in the EM volume, increasing the number of EMfields would increase the number of mappings, which can be timeconsuming and laborious. Additionally, to improve the accuracy withwhich the sensor location can be determined, precise measurements atmany (for example, thousands) of gridpoints within the EM volume may beneeded, which could make the generating of the mapping even more timeconsuming. Also, because of the potential variability during themanufacturing processes and tolerances of electrical equipment, themapping process may need to be completed for each new antenna that isproduced and for each electromagnetic navigation system installation.

Given the foregoing, a need exists for improved systems and methods forgenerating a map for electromagnetic navigation and identifying alocation and/or an orientation of a sensor based on the map.

SUMMARY

The present disclosure is related to systems and methods for generatinga map of EM field strength, for example, a high density (HD) map, forelectromagnetic navigation and identifying a sensor location and/ororientation based on the map. In one example, the HD map has a greater(e.g., finer) gridpoint resolution (that is, more gridpoints) in the EMvolume than that of a low density (LD) grid in the EM volume accordingto which EM field strength measurements are taken and stored in a LDmap. The HD map, in some aspects, is generated based on the previouslygenerated LD map of measured EM field strength and also based on EMfield strength calculations based, for instance on geometricconfigurations of antennas in an antenna assembly. In this manner, thelocation and/or the orientation of the sensor navigated within thepatient's body can be accurately identified without the need to take EMfield strength measurements at each of the many gridpoints of the HD mapwithin the EM volume. This can enable the use of a small-sized sensor inEMN procedures while minimizing any increased burden of map generation.

In accordance with one aspect of the present disclosure, a method isprovided for generating a high density (HD) map for identifying alocation and/or an orientation of an electromagnetic (EM) sensor withinan EM volume in which an EM field is generated by way of an antennaassembly. The method includes receiving a measured EM field strength ateach gridpoint of a first set of gridpoints of the EM volume from ameasurement device. An EM field strength at each gridpoint of a secondset of gridpoints of the EM volume is calculated based on a geometricconfiguration of an antenna of the antenna assembly. The HD map isgenerated based on the measured EM field strength at each gridpoint ofthe first set of gridpoints and the calculated EM field strength at eachgridpoint of the second set of gridpoints.

In another aspect of the present disclosure, the antenna assemblygenerates at least six EM waveforms as components of the EM field.

In a further aspect of the present disclosure, the EM field strength iscalculated along a three axes coordinate system for each of the at leastsix EM waveforms.

In yet another aspect of the present disclosure, the EM field strengthis measured by way of a sensor having three coils corresponding to thethree axes, respectively.

In still another aspect of the present disclosure, the second set ofgridpoints includes each gridpoint of the first set of gridpoints.

In another aspect of the present disclosure, the generating the HD mapincludes calculating an error between the measured EM field strength andthe calculated EM field strength, at each gridpoint of the first set ofgridpoints. An error for each gridpoint of the second set of gridpointsis interpolated based on the calculated error at each gridpoint of thefirst set of gridpoints. The interpolated error and the calculated EMfield strength at each gridpoint of the second set of gridpoints areadded to generate the HD map

In a further aspect of the present disclosure, the error is calculatedbased on a difference between the measured EM field strength and thecalculated EM field strength at each gridpoint of the first set ofgridpoints.

In yet another aspect of the present disclosure, the error is based onat least one of an L1 or L2 norm of differences between the measured EMfield strength and the calculated EM field strength along the threeaxes.

In still another aspect of the present disclosure, the method furtherincludes calculating a pseudo-inverse of the calculated EM fieldstrength at each gridpoint of the second set of gridpoints.

In another aspect of the present disclosure, the HD map further includesthe pseudo-inverse of the calculated EM field strength at each gridpointof the second plurality of gridpoints.

In accordance with another aspect of the present disclosure an apparatusis provided for generating an HD map for identifying a location and/oran orientation of an EM sensor within an EM volume in which an EM fieldis generated by way of an antenna assembly. The apparatus includes aprocessor and a memory storing processor-executable instructions that,when executed by the processor, cause the processor to receive, from ameasurement device, a measured EM field strength at each gridpoint of afirst set of gridpoints of the EM volume. An EM field strength at eachgridpoint of a second set of gridpoints of the EM volume is calculatedbased on a geometric configuration of at least one antenna of theantenna assembly. The HD map is generated based on the measured EM fieldstrength at each gridpoint of the first set of gridpoints and thecalculated EM field strength at each gridpoint of the second set ofgridpoints.

In another aspect of the present disclosure, the antenna assemblygenerates at least six EM waveforms as components of the EM field.

In still another aspect of the present disclosure, the EM field strengthis calculated along a three axes coordinate system for each of the atleast six EM waveforms.

In a further aspect of the present disclosure, the EM field strength ismeasured with a sensor having three coils corresponding to the threeaxes, respectively.

In yet another aspect of the present disclosure, the second set ofgridpoints includes each gridpoint of the first set of gridpoints.

In another aspect of the present disclosure, the generating of the HDmap includes calculating an error between the measured EM field strengthand the calculated EM field strength, at each gridpoint of the first setof gridpoints. An error for each gridpoint of the second plurality ofgridpoints is interpolated based on the calculated error at eachgridpoint of the first plurality of gridpoint. The interpolated errorand the calculated EM field strength at each gridpoint of the secondplurality of gridpoints are added to generate the HD map.

In yet another aspect of the present disclosure, the error is calculatedbased on a difference between the measured EM field strength and thecalculated EM field strength at each gridpoint of the first set ofgridpoints.

In a further aspect of the present disclosure, the error is based on anL1 and/or L2 norm of differences between the measured EM field strengthand the calculated EM field strength along the three axes.

In still another aspect of the present disclosure, the memory furtherstores instructions that, when executed by the processor, cause theprocessor to calculate a pseudo-inverse of the calculated EM fieldstrength at each gridpoint of the second set of gridpoints.

In another aspect of the present disclosure, the HD map further includesthe pseudo-inverse of the calculated EM field strength at each gridpointof the second set of gridpoints.

In accordance with another aspect of the present disclosure, a method isprovided for identifying a location and/or an orientation of an EMsensor navigated within an EM volume. The method includes retrieving,from a memory, a calculated EM field strength at each gridpoint of asecond set of gridpoints of the EM volume. An EM field is generated byway of an antenna assembly. A measured EM field strength is receivedfrom the EM sensor. A first gridpoint among a first set of gridpoints ofthe EM volume is identified based on the measured EM field strength anda HD map. The location and/or the orientation of the EM sensor areidentified based on the HD map, using the first gridpoint as an initialcondition. The second set of gridpoints includes the first plurality ofgridpoints.

In another aspect of the present disclosure, the antenna assemblyincludes at least six antennas, each of the antennas including multipleloops.

In yet another aspect of the present disclosure, the multiple loops havea geometric configuration.

In a further aspect of the present disclosure, the HD map includes acalculated EM field strength for each gridpoint of the second set ofgridpoints in the EM volume.

In still another aspect of the present disclosure, the calculated EMfield strength is based on the respective geometric configurations ofthe at least six antennas.

In another aspect of the present disclosure, the HD map further includesa pseudo-inverse of the calculated EM field strength at each gridpointof the second plurality of gridpoints.

In yet another aspect of the present disclosure, the identifying thefirst gridpoint includes identifying an orientation vector {right arrowover (n)}_((a,b,c)), where (a,b,c) is a gridpoint in the first set ofgridpoints, satisfying the following condition: {right arrow over(n)}_((a,b,c))≈{right arrow over (B)}_((a,b,c)) ⁻¹·V, where {right arrowover (B)}_((d,e,f)) ⁻¹ is a pseudo-inverse of {right arrow over(B)}_((a,b,c)), which is a calculated EM field strength at gridpoint(a,b,c) in the HD map. A difference between {right arrow over(B)}_((a,b,c))·{right arrow over (B)}_((a,b,c)) and V is calculating. Agridpoint (A,B,C), from among the first set of gridpoints, where adifference between {right arrow over (B)}_((a,b,c))·{right arrow over(n)} and V is the smallest, is selected, as the first gridpoint.

In a further aspect of the present disclosure, the identifying thelocation and/or the orientation includes identifying an orientationvector {right arrow over (n)}_((d,e,f)), where (d,e,f) is a gridpoint inthe second set of gridpoints and is located nearby (e.g. within apredetermined distance) from the first gridpoint (A,B,C), satisfying thefollowing condition: {right arrow over (n)}_((d,e,f))≈{right arrow over(B)}_((d,e,f))·V, where {right arrow over (B)}_((d,e,f)) is apseudo-inverse of {right arrow over (B)}_((d,e,f)) which is a calculatedEM field strength at gridpoint (d,e,f) in the HD map. A differencebetween {right arrow over (B)}_((d,e,f))·{right arrow over(n)}_((d,e,f)) and V is calculated. A second gridpoint (D,E,F) fromamong the second set of gridpoints, where a difference between {rightarrow over (B)}_((D,E,F))·{right arrow over (n)}_((D,E,F)) and V is thesmallest, is selected.

In still another aspect of the present disclosure, {right arrow over(n)}_((D,E,F)) is related to the orientation of the EM sensor.

In another aspect of the present disclosure, the second gridpoint(D,E,F) is the location of the EM sensor.

In accordance with another aspect of the present disclosure, a system isprovided for identifying a location and/or an orientation of an EMsensor navigated within an EM volume. The system includes an antennaassembly, the EM sensor, a processor, and a memory. The antenna assemblyis configured to radiate an EM field within the EM volume. The EM sensoris configured to measure an EM field strength based on the radiated EMfield. The memory stores a calculated EM field strength at eachgridpoint of a second set of gridpoints of the EM volume. The memoryalso stores processor-executable instructions that, when executed by theprocessor, cause the processor to retrieve, from the memory, thecalculated EM field strength at each gridpoint of the second set ofgridpoints. A first gridpoint among a first set of gridpoints of the EMvolume is identified based on the measured EM field strength and the HDmap. The location and/or the orientation of the EM sensor are identifiedbased on the HD map, using the first gridpoint as an initial condition.The second set of gridpoints includes the first set of gridpoints.

In a further aspect of the present disclosure, the antenna assemblyincludes at least six antennas, each of the antennas including aplurality of loops.

In still another aspect of the present disclosure, the plurality ofloops has a geometric configuration.

In another aspect of the present disclosure, the HD map includes acalculated EM field strength at each gridpoint of the second set ofgridpoints in the EM volume.

In yet another aspect of the present disclosure, the calculated EM fieldstrength is based on the respective geometric configurations of the atleast six antennas.

In another aspect of the present disclosure, the HD map further includesa pseudo-inverse of the calculated EM field strength at each gridpointof the second set of gridpoints.

In another aspect of the present disclosure, the identifying the firstgridpoint includes identifying an orientation vector {right arrow over(n)}_((a,b,c)), where (a,b,c) is a gridpoint in the first set ofgridpoints, satisfying the following condition: {right arrow over(n)}_((a,b,c))≈{right arrow over (B)}_((a,b,c)) ⁻¹·V, where {right arrowover (B)}_((d,e,f)) ⁻¹ is a pseudo-inverse of {right arrow over(B)}_((a,b,c)), which is a calculated EM field strength at gridpoint(a,b,c) in the HD map. A difference between {right arrow over(B)}_((a,b,c))·{right arrow over (n)}_((a,b,c)) and V is calculated. Agridpoint (A,B,C) from among the first plurality of gridpoints, where adifference between {right arrow over (B)}_((a,b,c))·{right arrow over(n)} and V is the smallest, is selected as the first gridpoint.

In yet another aspect of the present disclosure, the identifying thelocation and/or the orientation includes identifying an orientationvector {right arrow over (n)}_((d,e,f)), where (d,e,f) is a gridpoint inthe second set of gridpoints and is located nearby (e.g., within apredetermined distance from) the first gridpoint (A,B,C), satisfying thefollowing condition: {right arrow over (n)}_((d,e,f))≈{right arrow over(B)}_((d,e,f)) ⁻¹·V, where {right arrow over (B)}_((d,e,f)) ⁻¹ is apseudo-inverse of {right arrow over (B)}_((d,e,f)), which is acalculated EM field strength at gridpoint (d,e,f) in the HD map. Adifference between {right arrow over (B)}_((d,e,f))·{right arrow over(n)}_((d,e,f)) and V is calculated. A second gridpoint (D,E,F) fromamong the second plurality of gridpoints, where a difference between{right arrow over (B)}_((D,E,F))·{right arrow over (n)}_((D,E,F)) and Vis the smallest is selected.

In another aspect of the present disclosure, {right arrow over(n)}_((D,E,F)) is related to the orientation of the EM sensor.

In a further aspect of the present disclosure, the second gridpoint(D,E,F) is the location of the EM sensor.

Any of the aspects and embodiments of the present disclosure may becombined without departing from the scope of the present disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

Objects and features of the presently disclosed systems and methods willbecome apparent to those of ordinary skill in the art when descriptionsof various embodiments are read with reference to the accompanyingdrawings, of which:

FIG. 1 shows an example electromagnetic navigation (EMN) system, inaccordance with the present disclosure;

FIG. 2 is a block diagram of a portion of the EMN system of FIG. 1, inaccordance with the present disclosure;

FIG. 3 is a graphical illustration of example low density measurementsand related curves, in accordance with the present disclosure;

FIG. 4 is a flowchart illustrating an example method for generating ahigh density map, in accordance with the present disclosure;

FIG. 5 is a flowchart illustrating an example method for identifying alocation and/or an orientation of a sensor, in accordance with thepresent disclosure;

FIG. 6 is a graphical illustration of an example error function, havingmultiple local minima, of a discrepancy between a measurement value anda calculated value, in accordance with the present disclosure; and

FIG. 7 is a block diagram of a computing device for use in variousembodiments of the present disclosure.

DETAILED DESCRIPTION

The present disclosure is related to systems and methods for generatinga high density (HD) map and identifying a location and/or an orientationof a sensor, which may include at least one coil, based on the HD map.In some aspects, the respective geometric configurations the antennasenable automated and highly repeatable processes for reproducing suchantennas and/or for mathematically calculating the expected ortheoretical EM strength at every HD gridpoint within an EM volume (forinstance, where the antennas have geometric configurations based onlinear portions of printed circuit board (PCB) traces, which facilitateuse of the superposition principle in computing the total contributionof the fields generated by way of each antenna to the total combined EMfield within the volume). These mathematical calculations may becombined with actual measurements made in a coarse coordinate system,which includes fewer gridpoints than the number of gridpoints used forthe mathematically calculated EM strength. In this way, the time and/orcost related to making the measurements can be lowered and a HD map canbe generated and used in a repeatable, efficient, and cost-effectivemanner.

Further, the present disclosure is related to systems and methods foridentifying a location and/or an orientation of an EM sensor by usingthe HD map. In general, the EM sensor senses EM strengths, and an EMNsystem compares the sensed EM strengths with the expected EM strengthsof the HD map and identifies the location and the orientation of the EMsensor.

In an aspect of the present disclosure, a fine coordinate system (e.g.,a HD coordinate system or set of gridpoints) is used to describe acoordinate system of the EM volume, which includes more gridpoints thanthose in a coarse coordinate system (e.g., a LD coordinate system or setof gridpoints) of the EM volume. In some aspects, every gridpoint of thecoarse coordinate system may be included in the fine coordinate system.In general, the coarse coordinate system is utilized for actual EM fieldstrength measurements and the fine coordinate system is utilized formathematical calculations of EM field strength.

FIG. 1 illustrates an example electromagnetic navigation (EMN) system100, which is configured to identify a location and/or an orientation ofa medical device, or sensor thereof, navigating (e.g., to a target)within the patient's body by using an antenna assembly, which includes aplurality of antennas and generates EM fields. The EMN system 100 isfurther configured to augment CT, MRI, or fluoroscopic images innavigation through patient's body toward a target of interest, such as adeceased portion in a luminal network of a patient's lung.

The EMN system 100 includes a catheter guide assembly 110, abronchoscope 115, a computing device 120, a monitoring device 130, an EMboard 140, a tracking device 160, and reference sensors 170. Thebronchoscope 115 is operatively coupled to the computing device 120 andthe monitoring device 130 via a wired connection (as shown in FIG. 1) orwireless connection (not shown).

The bronchoscope 115 is inserted into the mouth of a patient 150 andcaptures images of the luminal network of the lung. In the EMN system100, inserted into the bronchoscope 115 is a catheter guide assembly 110for achieving access to the periphery of the luminal network of the lungof the patient 150. The catheter guide assembly 110 may include anextended working channel (EWC) 111 with an EM sensor 112 at the distalportion of the EWC 111. A locatable guide catheter (LG) may be insertedinto the EWC 111 with another EM sensor at the distal portion of the LG.The EM sensor 112 at the distal portion of the EWC 111 or the LG is usedto identify a location and/or an orientation of the EWC 111 or the LGwhile navigating through the luminal network of the lung. Due to thesize restriction in the EWC 111 or the LG, in some embodiments, the EMsensor 112 may include only one single coil for detecting EM strength ofan EM field over the patient 150. However, the number of coils in the EMsensor is not limited to one but may be two or more.

The computing device 120, such as, a laptop, desktop, tablet, or othersimilar computing device, includes a display 122, one or more processors124, memory 126, an AC current driver 127 for providing AC currentsignals to the antenna assembly 145, a network card 128, and an inputdevice 129. The particular configuration of the computing device 120illustrated in FIG. 1 is provided as an example, but otherconfigurations of the components shown in FIG. 1 as being included inthe computing device 120 are also contemplated. In particular, in someembodiments, one or more of the components (122, 124, 126, 127, 128,and/or 129) shown in FIG. 1 as being included in the computing device120 may instead be separate from the computing device 120 and may becoupled to the computing device 120 and/or to any other component(s) ofthe system 100 by way of one or more respective wired or wirelesspath(s) to facilitate the transmission of power and/or data signalsthroughout the system 100. For example, although not shown in FIG. 1,the AC current driver 127 may, in some example aspects, be separate fromthe computing device 120 and may be coupled to the antenna assembly 145and/or coupled to one or more components of the computing device 120,such as the processor 124 and the memory 126, by way of one or morecorresponding paths.

In some aspects, the EMN system 100 may also include multiple computingdevices, wherein the multiple computing devices are employed forplanning, treatment, visualization, or helping clinicians in a mannersuitable for medical operations. The display 122 may be touch-sensitiveand/or voice-activated, enabling the display 122 to serve as both inputand output devices. The display 122 may display two dimensional (2D)images or three dimensional (3D) model of a lung to locate and identifya portion of the lung that displays symptoms of lung diseases.

The one or more processors 124 execute computer-executable instructions.The processors 124 may perform image-processing functions so that the 3Dmodel of the lung can be displayed on the display 122 or locationalgorithm to identify a location and an orientation of the EM sensor112. In embodiments, the computing device 120 may further include aseparate graphic accelerator (not shown) that performs only theimage-processing functions so that the one or more processors 124 may beavailable for other programs. The memory 126 stores data and programs.For example, data may be mapping data for the EMN or any other relateddata such as a HD map, image data, patients' medical records,prescriptions and/or history of the patient's diseases.

The HD map may include a plurality of gridpoints in a fine coordinatesystem of the EM volume in which a medical device (e.g., the EWC 111,LG, treatment probe, or other surgical devices) is to be navigated, andexpected EM strengths at each of the plurality of gridpoints. When theEM sensor 112 senses EM strength at a point, the one or more processors124 may compare the sensed EM strength with the expected EM strengths inthe HD map and identify the location of the EM sensor 112 within the EMvolume. Further, an orientation of the medical device may be alsocalculated based on the sensed EM strength and the expected EM strengthsin the HD map.

As shown in FIG. 1, the EM board 140 is configured to provide a flatsurface for the patient 150 to lie upon and includes an antenna assembly145. When the patient 150 lies upon on the EM board 140, the antennaassembly 145 generates an EM field sufficient to surround a portion ofthe patient 150 or the EM volume. The antenna assembly 145 includes aplurality of antennas, each of which may include a plurality of loops.In one aspect, each antenna is configured to generate an EM waveformhaving a corresponding frequency. The number of antennas may be at leastsix. In an aspect, the number of antennas may be nine so that ninedifferent EM waveforms can be generated.

In another aspect, a time multiplexing method is employed in generatingthe EM waveforms. For example, the antennas of the antenna assembly 145may generate EM waveforms with the same frequency at different timesduring a period. In another aspect, frequency multiplexing method may beemployed, where each antenna generates EM waveform having a frequencydifferent from each other. In still another aspect, combination of thetime multiplexing and frequency multiplexing methods may be employed.The antennas are grouped into more than one group. Antennas in the samegroup generate EM waveforms having the same frequency but at differenttimes. Antennas in different groups may generate EM waveforms havingdifferent frequencies from each other. Corresponding de-multiplexingmethod is to be used to separate EM waveforms.

In an aspect, each antenna may have a geometric configuration (forinstance, where the antennas each have geometric configurations based onlinear portions of printed circuit board (PCB) traces or wires, whichfacilitate use of the superposition principle in computing the totalcontribution of the fields generated by way of each antenna to the totalcombined EM field within the volume) so that each portion of theplurality of loops can be expressed as mathematical relationship orequations, as described in further detail below. The magnetic field canthus be computed for each trace on the antenna and the contributionsfrom all traces can be summed. Based on this geometric configuration,expected EM strength at each gridpoint in the HD map can betheoretically or mathematically calculated. Additional aspects of suchexample antennas and methods of manufacturing the antennas are disclosedin U.S. patent application Ser. No. 15/337,056, entitled“Electromagnetic Navigation Antenna Assembly and ElectromagneticNavigation System Including the Same,” filed on Oct. 28, 2016, theentire contents of which are hereby incorporated by reference herein.

FIG. 2 shows a block diagram of a portion of the example electromagneticnavigation system 100 of FIG. 1, according to the present disclosure. Ingeneral, the computing device 120 of the EMN system 100 controls theantenna assembly 145 embedded in the EM board 140 to generate an EMfield, receives sensed results from the EM sensor 112, and determines alocation and an orientation of the EM sensor 112 in the EM volume.

The computing device 120 includes a clock 205, which generates a clocksignal used for generating the EM field and sampling the sensed results.Since the same clock signal is used for generating the EM field andsampling the sensed EM field, synchronization between the magnetic fieldgeneration circuitry (e.g., a waveform generator 210) and the waveformacquisition circuitry (e.g., a digitizer 215) may be achieved. In otherwords, when the clock 205 provides a clock signal to the waveformgenerator 210 and the digitizer 215, the EM waveforms generated by theantenna assembly 145 are digitally sampled by digitizer 215substantially at the same time. The digitizer 215 may include ananalog-to-digital converter (ADC, which is not shown) to digitallysample the sensed results and an amplifier (which is not shown) toamplify the magnitude of the sensed result so that the magnitude of thesensed results is within the operable range of the ADC. In an aspect,the digitizer 215 may include a pre-amplifier and post-amplifier so thatthe magnitude of the sensed result is amplified to be within theoperable range of the ADC by the pre-amplifier and digital samples arealso amplified to the magnitude of the sensed result by thepost-amplifier.

The demodulator 220 demodulates the digital samples to remove unwantedsignals (e.g., noises) and to restore the EM waveforms, which have beengenerated by the antenna assembly 145. The demodulator 220 may use timede-multiplexing method, frequency de-multiplexing method, or combinationof both to separate and identify the EM waveforms depending on themethod used by the antennas of the antenna assembly 145 to generate theEM waveforms, and to determine EM strength affected by each of theantenna of the antenna assembly 145.

For example, when the antenna assembly 145 includes six antennas, thedemodulator 220 is capable of identifying six EM strengths, which issensed by the EM sensor 112, for the six antennas, respectively. In acase when the number of antennas is nine, the outputs of the demodulator220 may be expressed in a form of a nine by one matrix. Based on themodulation method (e.g., time multiplexing, frequency multiplexing, or acombination thereof) utilized by the antennas, the demodulator 220demodulates the sensed result.

For example, when the antennas of the antenna assembly 145 utilizefrequency multiplexing, the demodulator 220 may use a set of finelytuned digital filters. Orthogonal frequency division multiplexing mayalso be utilized, in which the EM field and sampling frequencies arechosen in such a way that only the desired frequency from a specificantenna is allowed to pass while other frequencies are preciselystopped. In an aspect, the demodulator 220 may use a multiple taporthogonal frequency matched filter, in which the digital filter for aspecific frequency is tuned to the desired demodulation window.

The memory 126 may store data and programs related to identification ofa location and an orientation. The data includes a high density (HD) map225, which includes a plurality of gridpoints according to the finecoordinate system for the EM volume and expected EM strengths at thegridpoints. The HD map 225 may be based on three-axis coordinate system,where each gridpoint has three coordinates corresponding to the threeaxes, respectively. In this case, the expected EM strength at eachgridpoint may include one EM strength value along each axis for each EMwaveform. For example, if there are nine antennas generating ninedifferent EM waveforms, each of which having a separate frequency, andthree axes are x, y, and z axes, the expected EM strength may includenine EM strength values along the x axis, nine EM strength values alongthe y axis, and nine EM strength values along the z axis, at eachgridpoint. Such expected EM strength at each gridpoint may be expressedin a nine by three matrix form.

The HD map 225 may be made with computations 230, which includestheoretically calculated EM strengths at each axis at each gridpoint inthe fine coordinate system, and measurement 235, which includesmeasurements at each axis at each gridpoint in the coarse coordinatesystem. The fine coordinate system includes all the gridpoints in thecoarse coordinate system and the gridpoints of the fine coordinatesystem are more finely distributed than those of the coarse coordinatesystem. By using the geometric configuration of the antennas of theantenna assembly 145, measurement may not have to be made with the finecoordinate system. Rather, the measurement may be made in the coarsecoordinate system and theoretical computations may be made in the finecoordinate system. By combining the measurements 235 in the coarsecoordinate system with the theoretical computations 230 in the finecoordinate system, the HD map 225 may be generated. Generation of the HDmap 225 based on the measurement 235 and calculations 230 will bedescribed in further detail with respect to FIG. 4 below.

After passage of time or due to foreign objects near the EMN system 100,measurements by the EM sensor 112 or other hardware may need to becalibrated. Such calibration data may be also stored in the memory 126in a form of sensor calibration 240 and hardware calibration 245.

When the computing device 120 receives measurement data from the EMsensor 112 via the demodulator 220, the computing device 120 uses thelocation algorithm 250, which is also stored in the memory 126, with theHD map 225 to identify the location and the orientation of the EM sensor112 in the fine coordinate system. Identification of the location and/orthe orientation will be described in further detail with respect to FIG.5 below.

The location algorithm 250 may utilize any error minimization algorithmin identifying the location and the orientation of the EM sensor 112.For example, Levenberg-Marquardt algorithm may be employed to minimizeerrors between the expected EM strengths of the HD density map and thesensed results. Other error minimization methods or algorithms, which aperson having ordinary skill in the art can readily appreciate, may alsobe utilized without departing from the scope of this disclosure.

The memory 126 further includes applications 255, which can be utilizedby the computing device 120 of the EMN system 100 and which usesinformation regarding the location and the orientation of the EM sensor112. Such application 255 may be a displaying application, whichdisplays a graphical representation of a medical device, on which the EMsensor 112 is mounted or installed, at the location of the EM sensor 112and along the orientation of the EM sensor 112 in the EM volume, anapplication for treatment, which determines whether a medical device isnear a target of interest, or any other applications, which use thelocation and the orientation of the EM sensor 112.

FIG. 3 is a graphical illustration of multiple curves 320, 325, 330, and340, as well as discrete EM field strength measurements 315 a-315 itaken in the coarse coordinate system. The horizontal axis may representany axis among x, y, and z axes for the EM volume and the vertical axisrepresents a magnitude of EM field strengths. Gridpoints of the coarsecoordinate system are shown separated by 50 millimeters and measured EMstrengths at the gridpoints of the coarse coordinate system are shown asblack dots 315 a-315 i.

In some aspects, measurements may be taken at a specific hospital roomsand beds, where the EMN system 100 will be used, by way of a measurementjig, which includes three coils sensing an EM field strength in each ofthree different directions (e.g., x, y, and z axes). Examples of such ameasurement jig are disclosed by Provisional U.S. Patent Application No.62/237,084, entitled “Systems And Methods For Automated Mapping AndAccuracy-Testing,” filed on Oct. 5, 2015, the entire contents of whichare hereby incorporated herein by reference.

Based on the measurement values at LD gridpoints 315 a-315 i,interpolation may be used to generate first and second interpolatedcurves, 320 and 325. In one example, the first interpolated curve 320 isgenerated by a linear interpolation method and the second interpolatedcurve 325 is generated by B-spline interpolation. Calculated EMstrengths at gridpoints in the HD map are also interpolated to generatea third interpolated curve 330.

As shown in box 335, the first, second, and third interpolated curves320, 325, 330 are substantially different from each other between twogridpoints 315 h and 315 i. The first interpolated curve 320 is lowerthan the third interpolated curve 330, and the second interpolated curve325 is much higher than the second and third interpolated curves 325 and330. Due to these big differences, an error may be apparent if only oneof the three interpolated curves is used.

In order to minimize such differences, a fourth interpolated curve 340is used. The fourth curve 340 is generated by calculating discrepanciesbetween theoretical calculations and measurements at the LD gridpoints,such as 315 a-315 i, and interpolating the discrepancies for the HDgridpoints. By adding the fourth interpolated curve 340 to the thirdinterpolated curve 330 at the HD gridpoints, expected EM strength ateach gridpoints in the HD map is obtained and higher accuracy may beobtained. Detailed descriptions regarding how to generate the HD map isdescribed with respect to FIG. 4 below.

FIG. 4 is a flowchart illustrating an example method 400 for generatingan HD map based on theoretical calculations in the fine coordinatesystem and measurements in the coarse coordinate system. Measurementsmay be performed for the EM field generated by the antennas of theantenna assembly 145 of FIG. 1, each of which having a correspondinggeometric configuration. At 410, EM field measurements at all gridpointsin the coarse coordinate system are received from a measurement jig. Themeasurements may include three different measurements along three axesin the coarse coordinate system for each EM waveform. Thus, when thereare nine antennas, the measurements at one gridpoint may include threevalues for the three different axes and nine of three values for thenine different waveforms, respectively. In an aspect, these measurementsmay be in a form of nine by three matrix.

At 420, based on the geometric configuration of each antenna of theantenna assembly 145, EM field strength is theoretically ormathematically calculated. As described above, each antenna includes aplurality of loops, which have geometric configurations. In other words,each loop of the antenna can be expressed in a form of mathematicalequations or is made of simply linear portions. Thus, EM strength at anygridpoints in the fine coordinate system may be calculated by usingBiot-Savart-Laplace law as follows:

$\begin{matrix}{{{B(r)} = {\frac{µ_{0}}{4\;\pi}{\int\frac{{Idl} \times r^{\prime}}{{r^{\prime}}^{3}}}}},} & (1)\end{matrix}$where B(r) is the EM strength at the gridpoint r influenced by thelinear portion C, μ₀ is a magnetic constant of the vacuum permeability,4π×10−7 V·s/(A·m), ∫_(C) is a symbol of line integral on the linearportion C, I is the magnitude of the current passing through the linearportion C, dl is a vector whose magnitude is the length of thedifferential element of the linear portion C in the direction ofcurrent, r′ is a displacement vector from the differential element dl ofthe linear portion C to the gridpoint r, and × is a vector symbolrepresenting a cross product between two vectors. Since the linearportion C is a simple line and each loop of the antenna includesmultiple linear portions, total EM strength at the gridpoint r can be asum of the EM strengths influenced by all the linear portions of theantenna. Further, the EM strength at the gridpoint r by the pluralantennas is calculated in the same way. In other words, the total EMstrength at gridpoint r may include three calculated values for thethree different axes (e.g., x, y, and z axes) for one antenna, and nineof three calculated values for the nine antennas, in a case when thereare nine antennas. In an aspect, the calculated EM strength may beexpressed in a nine by three matrix form.

At 430, a discrepancy is calculated between the measured EM field andthe calculated EM field at each gridpoint in the coarse coordinatesystem. In an aspect, the discrepancy may be made smaller by calibratingparameters of the three coil sensor of the measurement jig, calibratingthe antennas, or calibrating parameters (e.g., frequencies or phases forthe waveform generator 210) of the computing device of the EMN system.

At 440, the calculated discrepancies at gridpoints in the coarsecoordinate system are interpolated for gridpoints in the fine coordinatesystem. Any method of interpolation including linear interpolation,b-spline interpolation, etc. may be used.

At 450, the interpolated discrepancies are added to the theoreticalcalculations of the EM field to from expected EM field strength at eachgridpoint in the fine coordinate system. The expected EM field strengthat each gridpoint may be in a form of a nine by three matrix in a casewhen there are nine separate EM waveforms. The HD map may furtherinclude a pseudo-inverse of the expected EM field strength at eachgridpoint in the HD map. This pseudo-inverse may be used in identifyinga location and an orientation of the EM sensor, which is described infurther detail with respect to FIG. 5 below.

FIG. 5 is a flowchart illustrating an example method 500 for identifyinga location and/or an orientation of an EM sensor, for example, mountedon a medical device, which is navigated within a patient's body, inaccordance with the present disclosure. The method 500 may be used whilea medical device navigates inside the patient's body. At 510, the HDmap, which includes expected EM field strength at each gridpoint of theHD map, is retrieved from a memory. As described above, the expected EMfield strengths are based on the theoretical computations in the finecoordinate system and measurements in the coarse coordinate system.

The EM sensor mounted on the medical device periodically transmitssensed EM field strength to an EMN computing device, which digitallysamples the sensed EM field strength. The EMN computing device measuresthe EM field strength based on the digital samples in step 520.

At 530, it is determined whether an initial location is set as aninitial condition. If it is determined that the initial location is notset, the EMN computing device compares all gridpoints in the coarsecoordinate system with the measured EM field strength, simply pickups,to find an approximate gridpoint in the coarse coordinate system nearthe location of the EM sensor, as an initial location, at 540.

In an embodiment, a following error function may be used at 540:

$\begin{matrix}{{E = {{\sum\limits_{\alpha = 1}^{N}\;\left( {{{\overset{\rightarrow}{B_{\alpha}}\left( {a,b,c} \right)} \cdot {\overset{\rightarrow}{n}\left( {a,b,c} \right)}} - V_{\alpha}} \right)^{2}} + {b\left( {{\overset{\rightarrow}{n}}^{2} - g^{2}} \right)}^{2}}},} & (2)\end{matrix}$where E is the error value, α is a counter, N is the number of antennas,(a,b,c) is a gridpoint in the coarse coordinate system, B_(α) (a,b,c) isa vector, one by three matrix, including an expected EM field strengthat (a,b,c) influenced by the α-th antenna, “·” is a symbol of dotproduct between two vectors, {right arrow over (n)}(a,b,c) is anorientation of the EM sensor, and V_(α) is a vector, one by one matrix,including a pickup influenced by the α-th antenna, b is a parameter tocontrol a gain weight, and g is a gain of the EM sensor. In an aspect,the parameter b is used when the gain of the EM sensor is known andfixed. The value for the parameter b may be chosen so as not to dominatethe error function E. In another aspect, when the gain of the EM sensoris not known, the parameter b may be set to zero or the gain squared,g², is assumed to be equal to the squared norm of the orientation vector{right arrow over (n)}.

In some examples, for convenience, the parameter b is assumed to bezero. In this case, the error function E becomes:

$\begin{matrix}{\sum\limits_{\alpha = 1}^{N}\;{\left( {{{\overset{\rightarrow}{B_{\alpha}}\left( {a,b,c} \right)} \cdot {\overset{\rightarrow}{n}\left( {a,b,c} \right)}} - V_{\alpha}} \right)^{2}.}} & (3)\end{matrix}$This error function is useful in identifying a location in the coarse orfine coordinate system. In an aspect, the error function is not limitedto the above equation (2) or (3) and can be any error function that aperson of ordinary skill in the art would readily appreciate withoutdeparting from the scope of this disclosure. For example, the errorfunction E may be:|{right arrow over (B)}(a,b,c)−V| ₁ or |{right arrow over (B)}(a,b,c)−V|₂,where ∥₁ or ∥₂ represents an L1 or L2 norm of the vector inside of thesymbol, respectively.

Referring briefly to FIG. 6, a curve of an error function along one axisis shown to illustrate how selection of an initial location may impactthe determination of a location that provides the global minimum of theerror. The horizontal axis represents a location along one axis (e.g.,x, y, or z axis) and the vertical axis represents a magnitude of theerror function. If the initial location is set to be near X₀ or X₁, thelocation giving a local minimum will be between X₀ and X₁. If theinitial location is set to be X₅ or X₆, the location giving a localminimum will be between X₅ and X₆. In contrast, if the initial locationis set to be one of X₂, X₃, or X₄, the location giving a local minimumwill be between X₃ and X₄, which gives the accurate global minimum.Thus, referring back to FIG. 5, in a case when there is no set initiallocation, the method 500 evaluates the error function at every gridpointin the coarse coordinate system to find a first gridpoint, whichprovides the global minimum, in step 540.

The error function E includes a term, the orientation vector {rightarrow over (n)}, which, at 540, may also be identified as follows:{right arrow over (n)}(a,b,c)={right arrow over (B)}(a,b,c)⁻¹ ·V  (4),where {right arrow over (B)}(a,b,c)⁻¹ is a pseudo-inverse of {rightarrow over (B)}(a,b,c), and V includes pickups. In one example, if thetotal number of antennas in the antenna assembly is nine, {right arrowover (B)}(a,b,c) is a nine by three matrix, {right arrow over(B)}(a,b,c)⁻¹ is a three by nine matrix, and V is a nine by one matrix.Thus, {right arrow over (B)}(a,b,c)⁻¹·V results in a three by onematrix, which is a column vector representing an orientation matrix,{right arrow over (n)}(a,b,c) at gridpoint (a,b,c) in the coarsecoordinate system.

Based on equation (3), the error function is evaluated. Errors of allgridpoints in the coarse coordinate system are compared with each other,and the gridpoint that provides the smallest error is selected as afirst gridpoint and is set as the initial location at 540. After theinitial location is set at 540, 550 follows. Also, at 530, when it isdetermined that the initial location is set, the step 550 is performed.

At 550, a predetermined number of gridpoints around the initial locationare selected to calculate the error function in the same way as inequation (2) or (3). For example, if the predetermined number ofgridpoints is three, three gridpoints from the initial location in bothdirections along x, y, and z axes form a cube, 7 by 7 by 7 gridpoints.Thus, 343 gridpoints are selected to calculate the error function, andone among the selected gridpoints, which provides the smallest error, isselected as a second gridpoint, i.e., the location of the EM sensor. Thecorresponding orientation vector is also set as the orientation of theEM sensor in step 550. The second gridpoint is set as the initiallocation in step 560.

According to one aspect, in step 540, the error may be compared with apredetermined threshold. If the error is less than the predeterminedthreshold, that gridpoint is selected as the second gridpoint or thelocation of the EM sensor and corresponding orientation vector isselected as the orientation of the EM sensor.

In step 570, it is determined whether the target has been reached. Whenit is determined that the target has not been reached, steps 520-570 arerepeated until the target is reached. Otherwise, the method 500 ends.

Turning now to FIG. 7, there is shown a block diagram of a computingdevice 700, which can be used as the computing device 120 of the EMNsystem 100, the tracking device 160, or a computer performing the method400 of FIG. 4 or the method 500 of FIG. 5. The computing device 700 mayinclude a memory 702, a processor 704, a display 706, network interface708, an input device 710, and/or output module 712.

The memory 702 includes any non-transitory computer-readable storagemedia for storing data and/or software that is executable by theprocessor 704 and which controls the operation of the computing device700. In an embodiment, the memory 702 may include one or moresolid-state storage devices such as flash memory chips. Alternatively orin addition to the one or more solid-state storage devices, the memory702 may include one or more mass storage devices connected to theprocessor 704 through a mass storage controller (not shown) and acommunications bus (not shown). Although the description ofcomputer-readable media contained herein refers to a solid-statestorage, it should be appreciated by those skilled in the art thatcomputer-readable storage media can be any available media that can beaccessed by the processor 704. That is, computer readable storage mediainclude non-transitory, volatile and non-volatile, removable andnon-removable media implemented in any method or technology for storageof information such as computer-readable instructions, data structures,program modules or other data. For example, computer-readable storagemedia include RAM, ROM, EPROM, EEPROM, flash memory or other solid statememory technology, CD-ROM, DVD, Blu-Ray or other optical storage,magnetic cassettes, magnetic tape, magnetic disk storage or othermagnetic storage devices, or any other medium which can be used to storethe desired information and which can be accessed by the computingdevice 700.

The memory 702 may store application 716 and data 714. The application716 may, when executed by the processor 704, cause the display 706 topresent user interface 718 on its screen.

The processor 704 may be a general purpose processor, a specializedgraphic processing unit (GPU) configured to perform specific graphicsprocessing tasks while freeing up the general purpose processor toperform other tasks, and/or any number or combination of suchprocessors.

The display 706 may be touch-sensitive and/or voice-activated, enablingthe display 706 to serve as both an input and output device.Alternatively, a keyboard (not shown), mouse (not shown), or other datainput devices may be employed.

The network interface 708 may be configured to connect to a network suchas a local area network (LAN) consisting of a wired network and/or awireless network, a wide area network (WAN), a wireless mobile network,a Bluetooth network, and/or the internet. For example, the computingdevice 700 may receive measurement data and variables, and perform themethod 400 of FIG. 4 to generate a HD map. The computing device 700 mayreceive updates to its software, for example, application 716, vianetwork interface 708. The computing device 700 may also displaynotifications on the display 706 that a software update is available.

In another aspect, the computing device 700 may receive computedtomographic (CT) image data of a patient from a server, for example, ahospital server, internet server, or other similar servers, for useduring surgical ablation planning. Patient CT image data may also beprovided to the computing device 700 via a removable memory.

Input device 710 may be any device by means of which a user may interactwith the computing device 700, such as, for example, a mouse, keyboard,foot pedal, touch screen, and/or voice interface.

Output module 712 may include any connectivity port or bus, such as, forexample, parallel ports, serial ports, universal serial busses (USB), orany other similar connectivity port known to those skilled in the art.

The application 716 may be one or more software programs stored in thememory 702 and executed by the processor 704 of the computing device700. During generation of the HD map, one or more software programs inthe application 716 may be loaded from the memory 702 and executed bythe processor 704 to generate the HD map. In an embodiment, during anavigation phase, one or more programs in the application 716 may beloaded, identify the location and the orientation of an EM sensormounted on a medical device, and display the medical device at thelocation along the orientation on a screen overlaid with other imagingdata, such as CT data or a three dimensional model of a patient. Inanother embodiment, during a treatment phase, one or more programs inthe application 716 may guide a clinician through a series of steps toidentify a target, size the target, size a treatment zone, and/ordetermine an access route to the target for later use during theprocedure phase. In some other embodiments, one or more programs in theapplication 716 may be loaded on computing devices in an operating roomor other facility where surgical procedures are performed, and is usedas a plan or map to guide a clinician performing a surgical procedure byusing the information regarding the location and the orientation.

The application 716 may be installed directly on the computing device700, or may be installed on another computer, for example a centralserver, and opened on the computing device 700 via the network interface708. The application 716 may run natively on the computing device 700,as a web-based application, or any other format known to those skilledin the art. In some embodiments, the application 716 will be a singlesoftware program having all of the features and functionality describedin the present disclosure. In other embodiments, the application 716 maybe two or more distinct software programs providing various parts ofthese features and functionality. For example, the application 716 mayinclude one software program for generating a HD map, another one foridentifying a location and an orientation, and a third program fornavigation and treatment program. In such instances, the varioussoftware programs forming part of the application 716 may be enabled tocommunicate with each other and/or import and export various dataincluding settings and parameters.

The application 716 may communicate with a user interface 718 whichgenerates a user interface for presenting visual interactive features toa user, for example, on the display 706 and for receiving input, forexample, via a user input device. For example, user interface 718 maygenerate a graphical user interface (GUI) and output the GUI to thedisplay 706 for viewing by a user.

In a case that the computing device 700 may be used as the EMN system100, the control workstation 102, or the tracking device 160, thecomputing device 700 may be linked to the display 130, thus enabling thecomputing device 700 to control the output on the display 130 along withthe output on the display 706. The computing device 700 may control thedisplay 130 to display output which is the same as or similar to theoutput displayed on the display 706. For example, the output on thedisplay 706 may be mirrored on the display 130. Alternatively, thecomputing device 700 may control the display 130 to display differentoutput from that displayed on the display 706. For example, the display130 may be controlled to display guidance images and information duringthe surgical procedure, while the display 706 is controlled to displayother output, such as configuration or status information of anelectrosurgical generator 101 as shown in FIG. 1.

The application 716 may include one software program for use during theplanning phase, and a second software program for use during thetreatment phase. In such instances, the various software programsforming part of application 716 may be enabled to communicate with eachother and/or import and export various settings and parameters relatingto the navigation and treatment and/or the patient to share information.For example, a treatment plan and any of its components generated by onesoftware program during the planning phase may be stored and exported tobe used by a second software program during the procedure phase.

Although embodiments have been described in detail with reference to theaccompanying drawings for the purpose of illustration and description,it is to be understood that the inventive processes and apparatus arenot to be construed as limited. It will be apparent to those of ordinaryskill in the art that various modifications to the foregoing embodimentsmay be made without departing from the scope of the disclosure. Forexample, various steps of the methods described herein may beimplemented concurrently and/or in an order different from the exampleorder(s) described herein.

What is claimed is:
 1. A method for generating a high density (HD) map for identifying at least one of a location or an orientation of an electromagnetic (EM) sensor within an EM volume in which an EM field is generated by way of an antenna assembly, the method comprising: receiving a measured EM field strength at each gridpoint of a first plurality of gridpoints of the EM volume from a measurement device; calculating a theoretical EM field strength at each gridpoint of a second plurality of gridpoints of the EM volume based on a sum of theoretical EM field strength calculations from a plurality of linear portions of an antenna of the antenna assembly, the second plurality of gridpoints including each gridpoint of the first plurality of gridpoints and at least one additional gridpoint not included in the first plurality of gridpoints; and combining the measured EM field strength at each gridpoint of the first plurality of gridpoints with the theoretical EM field strength calculation at each gridpoint of the second plurality of gridpoints to generate the HD map.
 2. The method according to claim 1, wherein the antenna assembly generates at least six EM waveforms as components of the EM field.
 3. The method according to claim 2, wherein the theoretical EM field strength is calculated along a three axes coordinate system for each of the at least six EM waveforms.
 4. The method according to claim 3, wherein the EM field strength is measured by way of a sensor having three coils corresponding to the three axes, respectively.
 5. The method according to claim 1, wherein the generating the HD map includes: calculating, at each gridpoint of the first plurality of gridpoints, an error between the measured EM field strength and the theoretical EM field strength calculation; interpolating an error for each gridpoint of the second plurality of gridpoints based on the calculated error at each gridpoint of the first plurality of gridpoints; and adding the interpolated error to the theoretical EM field strength calculation at each gridpoint of the second plurality of gridpoints to generate the HD map.
 6. The method according to claim 5, wherein the error is calculated based on a difference between the measured EM field strength and the theoretical EM field strength calculation at each gridpoint of the first plurality of gridpoints.
 7. The method according to claim 5, wherein the error is based on at least one of an L1 or L2 norm of differences between the measured EM field strength and the theoretical EM field strength calculation along the three axes.
 8. The method according to claim 1, further comprising calculating a pseudo-inverse of the theoretical EM field strength calculation at each gridpoint of the second plurality of gridpoints.
 9. The method according to claim 8, wherein the HD map further includes the pseudo-inverse of the theoretical EM field strength calculation at each gridpoint of the second plurality of gridpoints.
 10. An apparatus for generating a high density (HD) map for identifying at least one of a location or an orientation of an electromagnetic (EM) sensor within an EM volume in which an EM field is generated by way of an antenna assembly, the apparatus comprising: a processor; and a memory storing processor-executable instructions that, when executed by the processor, cause the processor to: receive a measured EM field strength at each gridpoint of a first plurality of gridpoints of the EM volume from a measurement device; calculate a theoretical EM field strength at each gridpoint of a second plurality of gridpoints of the EM volume based on a sum of theoretical EM field strength calculations from a plurality of linear portions of an antenna of the antenna assembly, the second plurality of gridpoints including each gridpoint of the first plurality of gridpoints and at least one additional gridpoint not included in the first plurality of gridpoints; and combine the measured EM field strength at each gridpoint of the first plurality of gridpoints with the theoretical EM field strength calculation at each gridpoint of the second plurality of gridpoints to generate the HD map.
 11. The apparatus according to claim 10, wherein the antenna assembly generates at least six EM waveforms as components of the EM field.
 12. The apparatus according to claim 11, wherein the theoretical EM field strength is calculated along a three axes coordinate system for each of the at least six EM waveforms.
 13. The apparatus according to claim 12, wherein the EM field strength is measured with a sensor having three coils corresponding to the three axes, respectively.
 14. The apparatus according to claim 10, wherein generating the HD map includes: calculating, at each gridpoint of the first plurality of gridpoints, an error between the measured EM field strength and the theoretical EM field strength calculation; interpolating an error for each gridpoint of the second plurality of gridpoints based on the calculated error at each gridpoint of the first plurality of gridpoints; and adding the interpolated error to the theoretical EM field strength calculation at each gridpoint of the second plurality of gridpoints to generate the HD map.
 15. The apparatus according to claim 14, wherein the error is calculated based on a difference between the measured EM field strength and the theoretical EM field strength calculation at each gridpoint of the first plurality of gridpoints.
 16. The apparatus according to claim 14, wherein the error is at least one of an L1 or L2 norm of differences between the measured EM field strength and the theoretical EM field strength calculation along the three axes.
 17. The apparatus according to claim 10, wherein the memory further stores instructions that, when executed by the processor, cause the processor to calculate a pseudo-inverse of the theoretical EM field strength calculation at each gridpoint of the second plurality of gridpoints.
 18. The apparatus according to claim 17, wherein the HD map further includes the pseudo-inverse of the theoretical EM field strength calculation at each gridpoint of the second plurality of gridpoints.
 19. The method according to claim 1, wherein the first plurality of gridpoints is defined in a first coordinate system of the EM volume and the second plurality of gridpoints is defined in a second coordinate system of the EM volume different than the first coordinate system.
 20. The apparatus according to claim 10, wherein the first plurality of gridpoints is defined in a first coordinate system of the EM volume and the second plurality of gridpoints is defined in a second coordinate system of the EM volume different than the first coordinate system. 